Studies that investigated the relation between appraisal and emotion have largely focused on the linear effect of appraisal criteria on subjective feelings (e.g., the effect of appraised goal obstruction on anger). Emotional responding can be extended to include more than just feelings, however. Componential definitions of emotion also add motivation, physiology, and expression. Moreover, a linear model is not compatible with the idea held by many appraisal theorists that appraisal criteria interact to produce emotional responding. In the present study, we modeled adaptive nonlinear interaction effects of appraisal criteria on motivation, expression, and physiology simultaneously. We applied a combination of principal component analysis for data reduction and multivariate adaptive regression splines (MARS) for automatic interaction identification. Data were obtained from a large-scale cross-cultural study on emotion concepts conducted in 27 countries, which represented semantic profiles of component information in 24 common emotion words. Results of modeling indicated that (a) appraisal of relevance, familiarity, goal compatibility, coping potential, and suddenness showed main effects on component responses; (b) appraisals of agency and norm compatibility uniquely showed interaction effects on component responses; (c) interaction effects explained significant variance only in some component responses but not all; and (d) the emotion patterns simulated by the fitted MARS model could be clustered according to qualitative emotion categories.